Realaspen.com reports that when police arrived at the couple's Aspen, Colo., home Christmas Day after a reported scuffle, Mueller, 32, told three different officers that she and Sheen, 44, got into a heated argument two or three months before after she accused him of sleeping with prostitutes.

According to the three police reports, she claimed Sheen shoved her head into a piece of furniture, resulting in a head injury that required a CAT scan and treatment by multiple physicians.

Wrote Officer Rick Magnuson: "I asked [Sheen] if he ever harmed Mueller in the past. [Sheen] stated that approximately two months ago, in California, Mueller accused him of sleeping with prostitutes. [Sheen] stated that he denied this allegation, which escalated into a 'huge fight.' He added that when Mueller attempted to leave the argument, he grabbed her by the wrist, causing her to fall to the ground. [Sheen] added that Mueller hit the back of her head on a piece of furniture as she fell to the ground. [Sheen] stated that Mueller was injured when her head contacted the furniture. [Sheen] added that neither he nor Mueller reported this incident to law enforcement. [Sheen] added that Mueller received medical treatment for her head injury. [Sheen] added that the Mueller's injury was not intentional, adding that she accidentally hit her head as he was trying to restrain her."

When Magnuson asked Mueller about the California fight, she got "upset," he wrote in his report. "She was very adamant that [Sheen] intentionally hurt her by throwing her to the ground, like a 'rag doll.'"

As for Sheen's Christmas Day arrest, the reports reveal Sheen and Mueller -- who both had been drinking -- got into a fight because of the hit Train song "Drops of Jupiter."

According to the police reports, Sheen told officers that he and his daughter "share an affinity for both astronomy" and the Train tune.

"He bought two tracking telescopes; one for his daughter and one for him so they could both look at the same point in the universe at the same time, as a way of staying connected," Magnuson wrote. "[Sheen] added that Mueller was jealous of this relationship with his daughter. He stated that Mueller said, 'You have a song you share with your daughter, but not one with me.' [Sheen] replied, 'It's my daughter, can I have this moment?' [Sheen] was emotional while telling this story."

Sheen told officers the argument escalated as they began to "slap" at "each other's hands or wrists."

Last week, Sheen pleaded guilty to a misdemeanor assault charge in the domestic violence case.